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What is a factorial?

In maths, the factorial of a non-negative integer, is the product of all positive integers less than or equal to this non-negative integer.

The symbol for the factorial function is an exclamation mark after a number.

For example: 5!

So if you see something like 5! , you know that you will have to multiply the series of descending possitive integers.

For example:

5! = 5 * 4 * 3 * 2 * 1 = 120


4! = 4 * 3 * 2 * 1 = 24

Integers or whole numbers or naturalnumbers?

If you google around a bit you will notice that the definition of l” differs a bit from each other: : : :

The use of , , and in thesedefinitionsmeans that all the numbers used in factorials should not be decimals, negative numbers(-10 for example) or fractions.


Natural numbers : The numbers that you use to count with: 1, 2, 3, 4…and on and on. Zero is not a natural number.

Whole numbers : All the numbers are ‘whole’ — there are no fractions, negative numbers or decimals. The only difference between whole and natural numbers is that 0 is a whole number.

Integers : Positive and negative whole numbers, for example -6, 0, -200,1660, 2 etc.******************************************************************

But what About“0!”

IS there a 0! Does it exists? Can we use it?It has been agreed that zero factorial can be used and that 0! = 1.

I agree that it seems weird that multiplying no numbers together can give you one. Salman Khan from the Khan Academy explains the reasoning very well in this video.

Something interesting

We can calculate a factorial from the previous one. Have a look at this:1! = 12! = 2 * 1 = 23! = 3 * 2 * 1= 64! = 4 * 3 * 2 * 1= 245! = 5 * 4 * 3 * 2 * 1= 120

Note that 3! (6) times 4 = 24, or the factorial of 4!We continue in the same way and find that, 4! times 5 = 120, or 5!

And 6! is equal to 5! * 6 (120 * 6) = 720

So we can conclude that: n! = n × (n−1)!

The JavaScript function

Now for some JavaScript action! As always in coding, there is often more than one way to write a function. So let’s look at two options. The first one makes use of a recursion. A recursion means that .

If this looks for you like a loop inside a function, you are absolutely right. We can also calculate the factorial of a number with a for loop:

We start our loop at 2 because 1 is already taken care of with

I encourage you to copy the code in the console and play with it a bit.

Real lifeuse

Are factorials used in real life or are they just a mathematical exercise? Uh yes, factorials can be very useful. The number n! is the number of ways you can arrange n objects.

Let’s say that you have three dogs (Alpha, Beta, Charlie) and you want to see in how many ways you can arrange them in a line. 3! will give us 6 different ways. And if we write it out, we will find that it is indeed so:

A deck of cards can be shuffled in 52! ways.


As you can see, the numbers can get large very quickly.

I hoped that you have enjoyed learning about factorials. Next up are palindromes!

natural numbers
©Michele Westmorland/Corbis

Ecosystem services contribute to jobs, economic growth, health, and human well-being. Although we interact with ecosystems and ecosystem services every day, their linkage to climate change can be elusive because they are influenced by so many additional entangled factors. FAAERD Autumn Road Pumpkins Mens Fashion Lightweight Mesh Air Cushion Sneakers Basketball Sneakers buy sale online discount shop for free shipping extremely pay with visa cheap online 38Y95
Ecosystem perturbations driven by climate change have direct human impacts, including reduced water supply and quality, the loss of iconic species and landscapes, distorted rhythms of nature, and the potential for extreme events to overwhelm the regulating services of ecosystems. Even with these well-documented ecosystem impacts, it is often difficult to quantify human vulnerability that results from shifts in ecosystem processes and services. For example, although it is more straightforward to predict how precipitation will change water flow, it is much harder to pinpoint which farms, cities, and habitats will be at risk of running out of water, and even more difficult to say how people will be affected by the loss of a favorite fishing spot or a wildflower that no longer blooms in the region. A better understanding of how a range of ecosystem responses affects people – from altered water flows to the loss of wildflowers – will help to inform the management of ecosystems in a way that promotes resilience to climate change.

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Key Message 1: Water

Climate change impacts on ecosystems reduce their ability to improve water quality and regulate water flows.

Process for Developing Key Messages:

The key messages and supporting chapter text summarize extensive evidence documented in the Ecosystems Technical Input Report, . This foundational report evolved from a technical workshop held at the Gordon and Betty Moore Foundation in Palo Alto, CA, in January 2012 and attended by approximately 65 scientists. Technical inputs (127) on a wide range of topics related to ecosystems were also received and reviewed as part of the Federal Register Notice solicitation for public input.

Description of evidence base

The author team digested the contents of more than 125 technical input reports on a wide array of topics to arrive at this key message. The foundational Technical Input Report was the primary source used.

Studies have shown that increasing precipitation is already resulting in declining water quality in many regions of the country, particularly by increasing nitrogen loading. This is because the increases in flow can pick up and carry greater loads of nutrients like nitrogen to rivers.

One model for the Mississippi River Basin, based on a doubling of CO, projects that increasing discharge and nitrogen loading will lead to larger algal blooms in the Gulf of Mexico and a larger dead zone. The Gulf of Mexico is the recipient system for the Mississippi Basin, receiving all of the nitrogen that is carried downriver but not removed by river processes, wetlands, or other ecosystems.

Several models project that declining streamflow, due to the combined effects of climate change and water withdrawals, will cause local extinctions of fish and other aquatic organisms, particularly trout in the interior western U.S. (composite of 10 models, A1B scenario). The trout study is one of the few studies of impacts on fish that uses an emissions scenario and a combination of climate models. The researchers studied four different trout species. Although there were variations among species, their overall conclusion was robust across species for the composite model.

Water quality can also be negatively affected by increasing temperatures. There is widespread evidence that warmer lakes can promote the growth of harmful algal blooms, which produce toxins.

New information and remaining uncertainties

Recent research has improved understanding of the relative importance of the effects of climate and human actions (for example, fertilization) on nitrogen losses from watersheds, and how the interactions between climate and human actions (for example, water withdrawals) will affect fish populations in the west. However, few studies have projected the impacts of future climate change on water quality. Given the tight link between river discharge and pollutants, only areas of the U.S. that are projected to see increases in precipitation will see increases in pollutant transport to rivers. It is also important to note that pollutant loading – for example, nitrogen fertilizer use – is often more important as a driver of water pollution than climate.

Assessment of confidence based on evidence

Given the evidence base and uncertainties, there is confidence that climate change impacts on ecosystems reduce their ability to improve water quality and regulate water flows.

It is well established that precipitation and associated river discharge are major drivers of water pollution in the form of excess nutrients, sediment, and dissolved organic carbon (DOC) transport into rivers. Increases in precipitation in many regions of the country are therefore contributing to declines in water quality in those areas. However, those areas of the country that will see reduced precipitation may experience water-quality improvement; thus, any lack of agreement on future water-quality impacts of climate change may be due to locational differences.

Very High

Strong evidence (established theory, multiple sources, consistent results, well documented and accepted methods, etc.), high consensus


Moderate evidence (several sources, some consistency, methods vary and/or documentation limited, etc.), medium consensus


Suggestive evidence (a few sources, limited consistency, models incomplete, methods emerging, etc.), competing schools of thought


Inconclusive evidence (limited sources, extrapolations, inconsistent findings, poor documentation and/or methods not tested, etc.), disagreement or lack of opinions among experts

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Climate-driven factors that control water availability and quality are moderated by ecosystems. Land-based ecosystems regulate the water cycle and are the source of sediment and other materials that make their way to aquatic ecosystems (streams, rivers, lakes, estuaries, oceans, groundwater). Aquatic ecosystems provide the critically important services of storing water, regulating water quality, supporting fisheries, providing recreation, and carrying water and materials downstream (Ch. 25: Double Buckles Flat Heel Mid Calf Boots Black 37 outlet marketable Hfsql9
). Humans utilize, on average, the equivalent of more than 40% of renewable supplies of freshwater in more than 25% of all U.S. watersheds. Dolcis Dolcis Kenzie SlipOn Pale Pink discount best store to get buy cheap tumblr eastbay sale online pick a best online clearance 2015 Yygce
Freshwater withdrawals are even higher in the arid Southwest, where the equivalent of 76% of all renewable freshwater is appropriated by people. Floral FIC Dara Women Wide Width Dress Slingback with Flower Bow for Evening Size amp; Measurement Guides Gold for cheap pay with visa online sneakernews cheap price clearance get authentic genuine 6MNUtB
In that region, climate change has likely decreased and altered the timing of streamflow due to reduced snowpack and lower precipitation in spring, although the precipitation trends are weak due to large year-to-year variability, as well as geographic variation in the patterns (Ch. 3: Water ; Ch. 20: Southwest ). NIKE Womens Roshe Two Running Shoe Gym Red/White/Black get authentic cheap price cheap sale footlocker cheap sale find great vPEadQobI
Depriving ecosystems of water reduces their ability to provide water to people as well as for aquatic plant and animal habitat (see Figure 8.1) .

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Additionally, when Twitter outgrew Ruby on Rails, the company shined a spotlight on scalable Scala as a more efficient and cost-effective alternative. Finally, when Apple moved away from Objective-C to Swift, developers had to switch too. With iOS development becoming more streamlined and increasingly accessible, it’s clear many developers don’t want to be left behind.

Developer Tools at Work

Python is the one

JavaScript may be the most in-demand language by employers, but Python wins the heart of developers across all ages, according to our Love-Hate index. Python is also the most popular language that developers want to learn overall, and a significant share already knows it.

Which languages do developers prefer by age?

Python is known for its simplicity, readability, and vast possibilities of scientific libraries. It’s also growing as part of introductory computer science courses. There is an unusual generational trend among newer languages: Younger developers dislike newer languages (like Go, Kotlin, and Scala) more so than older developers. In fact, Go creates one of the greatest divides. Developers aged 18-24 don’t care for it, but 45-54 year-olds consider it one of their most loved languages. The inverse is true about JavaScript.

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This is interesting, since many of the newer languages, including Go, embody learnings from older languages. One of Go’s primary designers created C decades ago. There’s an innate thirst for knowledge among younger developers. They are more likely to learn languages across the board — even those that they dislike — than older developers. The latter would choose their pursuit more selectively, based on their experience and what they think will stand the test of time.

Developer Tools at Work

Node.js is the newest jam

Which frameworks do developers prefer by age?

Node.js wins as most loved framework by the largest share of developers. As the only method for backend JavaScript, Node.js is favored across all ages. As for front-end frameworks, we all know that AngularJS and React are in vogue. But it turns out this love is most common among younger generations.

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Developers between 45-54 years old ranked AngularJS and React much lower. On the other hand, the exact inverse is true about Vue.js. It’s not immediately clear why this is true. We’d love to learn thoughts from Vue.js developers on the differences in age Freetoes Multi Color Thong Flip Flop cheap 100% guaranteed clearance visit new hTXMIPF6R

Talent Attraction

Assessing skills proves to be the biggest hiring challenge, more than talent shortage

What’s the biggest challenge when hiring talent?

Which assessment tools do employers use most?

According to 7,000+ employers, resumes are still by far the most common way developers are assessed today. Our survey found that 81% of hiring managers use resumes as the first step in the applicant screening process. When asked what the biggest hiring challenge is, the same hiring managers said assessing skill is their number one problem — as opposed to lack of talent. Meanwhile, only 55% of developers said resumes were a good reflection of their abilities.

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